The batting average for a batter with 60 hits in 180 at-bats is 0.333.
The total differential when the number of hits increases to 62 and at-bats increase to 184 is 0.01.
The estimated new batting average is 0.343.
The batting average for a batter is calculated using the formula A = h/b, where h is the total number of hits and b is the total number of at-bats.
Given that the batter has 60 hits in 180 at-bats, we can calculate the batting average as follows:
Batting average = h/b = 60/180 = 0.3333
The batting average for this batter is 0.3333 or approximately 0.333.
To find the total differential when the number of hits increases to 62 and at-bats increase to 184, we can calculate the differential of the batting average:
dA = (∂A/∂h) * dh + (∂A/∂b) * db
Since the partial derivative (∂A/∂h) is equal to 1/b and (∂A/∂b) is equal to -h/b^2, we can substitute these values into the total differential equation:
dA = (1/b) * dh + (-h/b^2) * db
Substituting the given values dh = 62 - 60 = 2 and db = 184 - 180 = 4:
dA = (1/180) * 2 + (-60/180^2) * 4
= 0.0111 - 0.0011
= 0.01
Therefore, the total differential is 0.01.
To estimate the new batting average, we add the total differential to the original batting average:
New batting average = Batting average + Total differential
= 0.333 + 0.01
= 0.343
The estimated new batting average is approximately 0.343.
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-6x-27=6
give me the answer please .
Answer:
-5.5
Step-by-step explanation:
-6x - 27 = 6
+ 27 +27
-6x = 33
÷-6 ÷-6
x = - 5.5
I am pretty sure the awnser is -5.5 because -6 Multiplied by -5.5 Is 33. 33 minus 27 is 6
A Food Marketing Institute found that 27% of households spend more than $125 a week on groceries. Assume the population proportion is 0.27 and a simple random sample of 467 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.29? Answer =
Probability that "sample-proportion" of "households-spending" more than $125 per-week is less than 0.29 is 0.8340.
In order to calculate the probability that the sample-proportion of households spending more than $125 a week is less than 0.29, we use the sampling-distribution of sample-proportions, assuming the sample was selected using simple random sampling.
The Population-proportion (p) is = 0.27
Sample-size (n) is = 467,
Sample-proportion (p') is = 0.29,
To calculate the probability, we find the z-score corresponding to the sample proportion and then find the probability,
The formula to calculate the z-score is:
z = (p' - p)/√((p × (1 - p))/n),
Substituting the values,
We get,
z = (0.29 - 0.27)/√((0.27 × (1 - 0.27))/467),
z = 0.02/√((0.27 × 0.73) / 467),
z ≈ 0.97
We know that the probability associated with a z-score of 0.97 is 0.8340.
Therefore, the required probability is 0.8340.
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Can you answer it right now pls
Answer:
4 times 10 to the negative seventh power
Step-by-step explanation:
We can see that the decimal has 6 zeros before it, and then it’s 4.
since there are 7 digits after the decimal point, we put 10 to the negative seventh power.
that gives us 0.0000001
to get 0.0000004, we need to multiply ten to the negative seventh power (0.0000001) by 4
The answer is a. which is 4 x 10‐⁷
Mrs. Hinojosa had 75 feet of ribbon. If each of the 18 students in her
class gets an equal length of ribbon, how long will each piece be?
Write your answer
2. Using a whole number of feet and a whole number of inches
Consider the matrix A. A- Find the characteristic polynomial for the matrix A. (Write your answer in terms of 2) (1-x)(2²) Find the real eigenvalues for the matrix A
The characteristic polynomial for matrix A is (1-x)(2²), and the real eigenvalues for matrix A are 1 and 2.The characteristic polynomial for the matrix A can be written as (1-x)(2²), where x is the eigenvalue.
The real eigenvalues for matrix A can be found by setting the characteristic polynomial equal to zero and solving for x. Since the characteristic polynomial is a product of linear factors, the eigenvalues are the values of x that make each factor equal to zero.
In this case, we have two factors: (1-x) and (2²). Setting each factor equal to zero, we find that x = 1 and x = 2 are the real eigenvalues for matrix A.
To summarize, the characteristic polynomial for matrix A is (1-x)(2²), and the real eigenvalues are 1 and 2. The characteristic polynomial captures the relationship between the eigenvalues and the matrix A, while the real eigenvalues represent the values for which the matrix A has corresponding eigenvectors.
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Solve the initial value problem below using the method of Laplace transforms. y" - 12y' + 72y = 40 e 4 y(0) = 1, y'(0) = 10
To solve the given initial value problem using the method of Laplace transforms, we need to perform the following steps:
Step 1: Take the Laplace transform of both sides of the given differential equation.
Step 2: Solve for the Laplace transform of y.
Step 3: Take the inverse Laplace transform to obtain y.
Step 4: Use the initial conditions to find the constants in the solution obtained in Step 3.1.
Taking the Laplace transform of both sides of the given differential equation: L{y" - 12y' + 72y} = L{40e⁴}L{y" - 12y' + 72y} = 40L{e⁴}.
Taking Laplace transform of y" term L{y"} - 12L{y'} + 72L{y} = 40L{e⁴}.
Using the Laplace transform property of derivatives,
we get:s²Y(s) - sy(0) - y'(0) - 12[sY(s) - y(0)] + 72Y(s) = 40/(s - 4)
Simplifying the above equation, we get: s²Y(s) - s - 10 - 12sY(s) + 12 + 72Y(s) = 40/(s - 4)⇒ s²Y(s) - 12sY(s) + 72Y(s) = 40/(s - 4) + s + 2
Using partial fraction decomposition, we can write the right-hand side of the above equation as:40/(s - 4) + s + 2 = [10/(s - 4)] - [10/(s - 4)²] + s + 2
Now, the given equation becomes:
s²Y(s) - 12sY(s) + 72Y(s) = [10/(s - 4)] - [10/(s - 4)²] + s + 2
Taking the Laplace transform of y(0) = 1 and y'(0) = 10, we get: Y(s) = (10s + 2 + 1)/[s² - 12s + 72]
Applying partial fraction decomposition to find Y(s),
we get: Y(s) = [3/(s - 6)] - [1/(s - 6)²] + [7/(s - 6)²] + [1/(s - 6)]
Taking the inverse Laplace transform of Y(s), we get: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
Using the initial conditions y(0) = 1 and y'(0) = 10, we get: y(0) = 1 = 1 + 0 + 0 + 1, y'(0) = 10 = 18 - 3 + 7 + 1
Therefore, the solution to the given initial value problem is: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
Answer: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
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Solve for x , assume all segments that appear tangent are tangent.
Answer:
Step-by-step explanation:
x = 5
The value of x in the given angle is 5.
What is circle?A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.
Labelling the figure,
We have,
Measure of complete angle of circle = 360 degree
∠ABC = 360 - (81 + 74)
= 205 degree
Now from figure,
∠APE = (205 - 81 )/2
= 62 degree
Since we know that,
∠APE = 17x - 23
Therefore,
17x - 23 = 62
17x = 85
x = 5 degree,
Hence,
Required value is 5.
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Question is in picture
Answer: 1.7
Step-by-step explanation: We can use the pythagorean theorem!
A² + B² = C²
1² + B² = 2²
1 + B² = 4
4 - 1 = B²
3 = B²
√3 = B
1.7 = B
Hope this helps :)
Max gets a weekly allowance of $17. He spends $3 each week on snacks. He splits the rest of his allowance into equal amounts for his college fund and spending money. How much money does Max keep for spending money each week? $
Answer:
$7
Step-by-step explanation:
The amount max keeps for spending = 1/2(total allowance - amount he spends on snacks)
total allowance = $17
amount he spends on snacks = $3
Amount he would have for his college fund and spending money. = $17 - $3 = $14
Since he splits the amount equally between his college fund and spending money, the amount he would have for spending can be determined by dividing 14 by 2
$14/2 = $7
What's the greatest common factor 25x^2 and 100x^4y^2
Answer:
I D K
Step-by-step explanation:
Nita is making pizza.
She needs 3/4 cup of cheese to make one whole pizza .
She has 3/8
Nita can make exactly one whole pizza or less than or more than
Answer:
Less than
Step-by-step explanation:
To see how 3/4 compares to 3/8, give em the same denominator. The simplest way is to multiply 3/4 by 2. Multiply each the numerator and denominator by 2. That gives you 6/8. She needs 6/8 but only has 3/8, so less than a pizza.
If 491 households were surveyed out of which 343 households have internet fiber cable, what is the sample proportion of households without fiber cable is
The sample proportion of households without fiber cable can be calculated by subtracting the proportion of households with fiber cable from 1.
In this case, out of the 491 households surveyed, 343 households have internet fiber cable. To find the proportion of households without fiber cable, we subtract the proportion of households with fiber cable (343/491) from 1. The proportion of households without fiber cable is 1 - (343/491). Simplifying this expression, we get (491 - 343)/491 = 148/491.
Therefore, the sample proportion of households without fiber cable is 148/491, which is approximately 0.3012 or 30.12%. This means that in the surveyed sample, around 30.12% of households do not have internet fiber cable. It's important to note that this proportion represents the sample and not the entire population, as it is based on the households surveyed.
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A curve with the equation Sin(x) – y Cos(x) = y passes through two points A(nt, a) and B(a, b) (a
The equation of the curve as, (y - a) = (b - a) (x - nt) / (a - nt) which is a straight line passing through the two given points, A(nt, a) and B(a, b).
Given: Two points A (e.g., a) and B (a, b) are traversed by the curve whose equation is Sin(x) – y Cos(x) = y (a Solution: (sin x - y cos x) = y Taking y to the left, we get (sin x) = (y y cos x) Again, we can write y as (y) = (sin x) / (1 cos x) Simplifying this even further, we get (y) = (sin x / 2) / (cos x/2) Substituting the values of x = nt A( eg, a) and B( a, b), we get the condition in the structure, y - a = (b - a) (x - ex.)/( a-ex.)
Tackling the above condition, we get the condition bend which is a straight line going through two given focuses A (eg, a) and B(a, b). As a result, we obtain a curve in the form of an equation (y - a) = (b - a) (x - nt) / (a) - nt), which is a straight line that runs through the two points A(eg, a) and B(a, b) that have been given to us.
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If difference scores begin to pile up away from a sample mean difference score of Mp= 0, which of the following statements is true? a. The critical region is small.
b. The null hypothesis will likely be rejected. c. The sample size is large. d. The null hypothesis will likely fail to be rejected.
If difference scores begin to pile up away from a sample mean difference score of Mp= 0, the null hypothesis will likely be rejected. So, correct option is B.
This suggests that there is a likely effect or relationship between the variables being compared.
Option b. The null hypothesis will likely be rejected is the correct statement in this scenario. When the observed differences are consistently far from zero, it implies that the null hypothesis, which assumes no significant difference or effect, is unlikely to be true.
Thus, based on the evidence provided by the data, we would reject the null hypothesis in favor of an alternative hypothesis that suggests the presence of a difference or effect.
The critical region refers to the region of extreme values that would lead to rejecting the null hypothesis. While the size of the critical region can vary depending on the chosen significance level, it does not directly indicate the likelihood of rejecting the null hypothesis in this context.
Similarly, the sample size (option c) does not provide information about the likelihood of rejecting the null hypothesis in this situation.
So, correct option is B.
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Find the volume of the cylinder. Use 3.14 for T.
height of 1ft radius of 2ft
Answer:i don’t know yet give me a sec
Step-by-step explanation:
Answer:
12.56 cubic feet (ft^3)
Step-by-step explanation:
Area of the circular face of the cylinder = (pi)r^2, or (3.14)(2)^2.
This ends up being equal to 12.56. Multiply this by the height of the cylinder, 1, and you get 12.56, your final answer.
I would appreciate Brainliest, but no worries.
Find the missing side. round to the nearest tenth.
Answer:
14.6
Step-by-step explanation:
Sin (59) = x/17
17*sin (59) = x
17*0.857=14.57
The value of x in the triangle is x = 14.581
We have,
From the triangle,
using the sin function.
Now,
sin = perpendicular/hypotenuse
So,
sin 59 = x/17
Now,
To solve for x in the equation sin(59°) = x/17, we can use the properties of trigonometric functions and algebraic manipulation.
First, let's isolate x by multiplying both sides of the equation by 17:
17 x sin(59°) = x
Using a calculator to evaluate sin(59°), we find:
17 x 0.857167 = x
Therefore,
The value of x is x = 14.581
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Consider an upright cone that has a base radius of r and height h that has been obtained by revolving a triangular plane region (pictured below) about the y-axis. Apply the cylindrical shells method to con- Ty firm that the volume of the cone is V = arh. h + 0 r
By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.
Given that,
Consider an upright cone that was generated by rotating the triangular plane region shown in the image about the y-axis. It has a base radius of r and a height of h.
We have to apply the cylindrical shells method to confirm that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h
We know that,
By using the disk method,
V = [tex]\int\limits^b_a {\pi [f(x)]^2} \, dx[/tex]
Differentiating on both the sides,
dV = π[f(x)]² dx
Integrating on both sides with the limits 0 to h
[tex]\int\limits^h_0 { dV }= \int\limits^h_0 {\pi[f(x)]^2 }dx[/tex]
V = [tex]\int\limits^h_0 {\pi \frac{r^2x^2}{h^2} } \, dx[/tex]
V = [tex]\pi \frac{r^2}{h^2}\int\limits^h_0 {x^2 } \, dx[/tex]
V = [tex]\pi \frac{r^2}{h^2}[\frac{x^3}{3}]^h_0[/tex]
V = [tex]\pi \frac{r^2}{h^2}[\frac{h^3}{3}][/tex]
V = [tex]\frac{1}{3}[/tex]πr²h
Therefore, By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.
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The areas of the squares adjacent to two sides of a right triangle are shown below. What is the area of the squares adjacent to the third side of the triangle
Answer:
11 square units
Step-by-step explanation:
Find the diagram attached
First we need to find the side length of the square with known areas.
Area of a square = L²
L is the side length of the square
For the green square
44 = L²
Lg = √44
For the purple square
Ap = Lp²
33 = Lp²
Lp = √33
Get the length (L) of the unknown square using pythagoras theorem;
Lg² = L²+Lp²
(√44)² = L²+(√33)²
44 = L²+33
L² = 44-33
L² = 11
Since Al = L²
Hence the area of the square adjacent to the third side of the triangle is 11 square units
please help! no links please!
The value of x is: 75°
360° - 128° - 85° - 72° = 75°
18
A fruit salad was prepared containing 100 g of
acerola cherries, 100 g of kiwifruit, 300 g of
pineapple, and 200 g of strawberries. What is the
total amount of vitamin C, in grams, that is
contained in the listed fruits?
A)0.7g
B)2.069g
C)700g
D)2069g
Some pls help me I’ll give out brainliest please dont answer if you don’t know
Answer:
−
8
n
+
24
Step-by-step explanation:
Tell whether $x$ and $y$ are proportional. $x$ 0.25 0.5 0.75 $y$ 4 8 12
Answer:
x and y are proportional. Two quantities are proportional if there is a constant ratio between them. In this case, the ratio between y and x is always 16:
4/0.25=16
8/0.5=16
12/0.75=16
Since the ratio between y and x is always the same, x and y are proportional.
Step-by-step explanation:
answer this please
don't send a link
Answer:
Supplementary angles
Step-by-step explanation:
AEB and BEC form a straight line.
They add to 180 degrees
AEB+ BEC
150+30
180
That means that they are supplementary angles
Answer: https://www.wattpad.com/story/73852998-feathers-itachi-uchiha-deidara-x-reader-lemon
Step-by-step explanation:
If m3 is 52°, what is the measure of its vertical angle?
A.
128°
B.
38°
C.
52°
D.
142°
i need answer asap!
Answer:
C. 52 degrees
Step-by-step explanation:
Vertical angles share the same angle of measure.
16. Max is sitting in the stands at the baseball stadium. He catches a
and decides to throw it back to a player standing on first base. If the
horizontal distance from Max to the player is 61 feet and the ball travels 76
feet, what is the angle of depression from Max to the player?
Gina Wilson (All Things Algebra), 2016
20, 17, 14
Write donn
the
4 th
term
Answer:
11
Step-by-step explanation:
you subtract 3 every time, so 14-3 = 11
can someone actually help me with this please!
Answer:
y = -2x + 7
Step-by-step explanation:
When 2 lines are perpendicular, the relationship between their slopes m1 and m2 may be stated as
m1m2 = -1
Given the line
y = 1/2 x + 8
Comparing with the general equation of a line y = mx + c where m is the slope and c is the intercept
m = m1 = 1/2
Hence the slope of the perpendicular line m2
= -1/1/2
= -2
Given that the line passes through the points (1,5)
using the equation
y - y1 = m (x - x1)
y - 5 = -2(x - 1)
y = -2x +2 + 5
y = -2x + 7
Is (2, 3) a solution to the equation y = x - 1?
yes or no
and pls explain for i can lead this already
Answer: No
Step-by-step explanation: Because if you substitute the 2 for x and 3 for y it is not equal
Two cheeseburgers and one small order of fries contain a total of 1400 calories. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Find the caloric content of each item.
Let the calories of a cheeseburger be C, and the calories of a small order of fries be F. Using this notation: Two cheeseburgers and one small order of fries contain a total of 1400 calories. Calories in 2 cheeseburgers + Calories in 1 small order of fries = 14002C + F = 1400. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Calories in 3 cheeseburgers + Calories in 2 small orders of fries = 22603C + 2F = 2260. We can solve for C and F by solving these two equations for C and F using the method of elimination.
Let's double the first equation and subtract the second equation: 4C + 2F = 2800 -(3C + 2F = 2260). 1C = 540 C = 540. Calories in a cheeseburger = C = 540. Substituting this value of C into either of the two equations and solving for F gives us:2C + F = 14002(540) + F = 1400. F = 320. Calories in a small order of fries = F = 320. Therefore, two cheeseburgers contain 2C = 2(540) = 1080 calories, and one small order of fries contains F = 320 calories. Three cheeseburgers contain 3C = 3(540) = 1620 calories, and two small orders of fries contain 2F = 2(320) = 640 calories.
Answer: Calories in a cheeseburger = C = 540Calories in a small order of fries = F = 320. Calories in two cheeseburgers = 2C = 2(540) = 1080. Calories in three cheeseburgers = 3C = 3(540) = 1620. Calories in one small order of fries = F = 320Calories in two small orders of fries = 2F = 2(320) = 640.
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9. Let H be the set of all vectors of the form 3s. Find a 2s vector v in R3 such that H that H is a subspace of IR 3? Span {v). Why does this show 2t 10. Let H be the set of all vectors of the form 0.Show that H is a subspace of R3. (U'se the method of Exercise 9.) 11. Let W be the set of ali vectors of the formb where b and c are arbitrary. Find vectors u and v such that W Span (u, v. Why does this show that W is a subspace of R3? St 2s-t 4t 12 Let W be the set of all vectors of the form Show that W is a subspace of R4. (Use the method/of Exercise 11.)
9. H is a subspace of R3 as it contains a 2s vector [0, 2s, 0].
10. H is a subspace of R3 as it consists of the zero vector [0, 0, 0].
11. W is a subspace of R3 as it is spanned by the vectors [1,0,0] and [1,1,0].
12.W is a subspace of R4 as it is spanned by the vectors [1,2,0,0] and [0,-1,4,0].
9. To find a 2s vector v in R3 such that H is a subspace of R3, we can choose v = [0, 2s, 0]. This vector satisfies the condition of H being a subspace since it is of the form 2s, and any scalar multiple of v will also be of the form 2s, which is within H. Therefore, H is a subspace of R3.
0. Let H be the set of all vectors of the form [0, 0, 0]. To show that H is a subspace of R3, we can use the method from Exercise 9. By choosing v = [0, 0, 0],
we can see that H is closed under scalar multiplication and addition, as any scalar multiple or sum of the zero vector will still result in the zero vector. Therefore, H is a subspace of R3.
11. Let W be the set of all vectors of the form [b, c, 0], where b and c are arbitrary. To show that W is a subspace of R3, we need to find vectors u and v such that W is spanned by (u, v).
We can choose u = [1, 0, 0] and v = [0, 1, 0]. Any vector in W can be expressed as a linear combination of u and v, and therefore W is spanned by (u, v). This shows that W is a subspace of R3.
12. Let W be the set of all vectors of the form [s, 2s - t, 4t] in R4. To show that W is a subspace of R4, we can use the method from Exercise 11. By choosing u = [1, 2, 0, 0] and v = [0, -1, 4, 0],
we can observe that any vector in W can be expressed as a linear combination of u and v. Hence, W is spanned by (u, v), indicating that W is a subspace of R4.
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